Profile of Subra Suresh

PROFILE PROFILE Profile of Subra Suresh

Sandeep Ravindran, Science Writer

During his long and distinguished career, Subra Foundation (NSF) of the United States. Now President Suresh has made crucial contributions to the field of of Nanyang Technological University, Singapore, engineering. While finishing up high school in India in Suresh continues to push forward in research with his the 1970s, however, Suresh was not even sure of recent work on deforming nanoscale diamond. In his going to college, let alone becoming an engineer. Inaugural Article (1), Suresh and his colleagues show Nonetheless, Suresh decided to take a shot at the computationally that it is possible to make nanoscale entrance examination for the prestigious Indian Insti- diamond behave like a metal with respect to select tutes of Technology. “A month before my exam, I properties, which would open up a wide array of ap- bought a book to prepare and worked through some plications in microelectronics, optoelectronics, and practice questions and just thought, go try it,” Suresh solar energy. says. “To my surprise, I got in.” His degree in mechanical engineering from Indian Institutes of Technology Spanning Many Disciplines Madras would turn out to be the starting point of a After obtaining his bachelor’s degree at Indian Insti- wide-ranging research career. tutes of Technology Madras, a scholarship offer led Suresh’s research interests would eventually span Suresh to attend Iowa State University for a Master’s engineering, basic science, and medicine. His multi- degree in mechanical engineering. When he left for disciplinary work led to elected memberships in all the Massachusetts Institute of Technology (MIT) two three US National Academies: The National Academy years later for a doctorate, Suresh joined the materials of Engineering in 2002, the National Academy of Sci- group in mechanical engineering, beginning his foray ences in 2012, and the National Academy of Medicine into materials science. in 2013. After just a year and a half into his doctoral work at Suresh has held several prestigious positions, from MIT, Suresh’s thesis committee deemed he was ready being dean of Massachusetts Institute of Technology’s to receive a doctorate. “I was just stunned when they School of Engineering and president of Carnegie told me I was ready to defend my ScD [Doctor of Mellon University to leading the National Science Science] thesis,” he says. Suresh had finished so quickly that he was not yet sure about the next step. So, when his thesis advisor moved to the University of California, Berkeley, and offered him a postdoctoral fellowship, Suresh accepted. After two years at Berkeley, Brown University offered Suresh a faculty position. “They were looking for someone to bridge mechanical engineering and materials science, and they thought I would be the right candidate for it,” says Suresh. “That’s how I migrated more and more into materials science,” he says. Brown granted Suresh tenure in less than three years, and during his 10 years there Suresh worked mainly on structural materials, such as steel, aluminum, and ce- ramics, work that culminated in his first book, Fatigue of Materials (2). Before long, MIT approached him, looking for a materials science professor with a background in mechanical engineering. “They made me an offer I couldn’t say no to, and so I went back to MIT as the Subra Suresh. Image credit: Nanyang Technological University, Singapore. R. P. Simmons Professor in 1993,” says Suresh. With a

Published under the PNAS license. This is a Profile of a member of the National Academy of Sciences to accompany the member’s Inaugural Article, 10.1073/pnas.2013565117. First published October 5, 2020.

25192–25194 | PNAS | October 13, 2020 | vol. 117 | no. 41 www.pnas.org/cgi/doi/10.1073/pnas.2018742117 Downloaded at MIT LIBRARIES on October 30, 2020 joint appointment in materials science and mechanical several initiatives over the next four years. These engineering, Suresh changed his research focus from programs included the Global Learning Council to large structures to small ones. He worked mainly on accelerate the impact of technology-enhanced learn- microelectronics and film coatings, work that led to a ing, an ambitious infrastructure development effort, a second book, Thin Film Materials (3). Center for Entrepreneurship, and the Presidential In 2003, Suresh pivoted again, this time to bio- Fellowships and Scholarships Program to support top medical sciences and engineering. “We started look- students. During his tenure as president, Carnegie ing at red blood cells and the connection between Mellon University’s undergraduate freshman class in mechanical properties at the cellular and molecular the School of Computer Science comprised a record level, and human diseases, such as malaria and sickle 48% of women students, three times the United States cell anemia,” he says. Over the next several years, national average. Suresh and his research group published prolifically at the intersection of engineering and physiology (4–7). Improving the Performance of Diamonds In 2010, Suresh was offered a challenge on a dif- In 2017, Suresh was appointed president of Nanyang “ ferent scale. President Obama nominated me to be Technological University, Singapore. While helming a ” the director of the National Science Foundation, says major research university, he also began research on “ Suresh. That was a great honor when the White nanoscale diamonds. ” House called. “We had a hypothesis that materials often behave surprisingly differently at the nanoscale than at the Driving Innovation at the NSF macro- or even micro-scale,” says Suresh. In addition As director of the NSF, Suresh launched the Innova- to being the hardest material, diamond is extremely tion Corps (I-Corps), an initiative aimed at helping brittle. “If you try to break it, nothing will happen at researchers across the country commercialize their first until you impose a very high load, and then all of a “ discoveries from basic research. I felt that there was a sudden it will crack and break catastrophically,” says ’ lot of very good science that s funded by NSF with Suresh. “When we go to the nanoscale, things be- taxpayer funds that could potentially lead to compa- come stronger, there is more surface area per unit nies or economic value or patents, but that never sees volume, and the density of defects becomes smaller. the light of day,” he says. “I believe that any smart, So we thought nanodiamond might behave differently young person anywhere can come up with a brilliant than bulk diamond that you can buy in a store,” idea,” says Suresh. “But if you happen to be in a place says Suresh. where there’s no infrastructure for commercialization, In a 2018 study, Suresh and his colleagues grew no matter how good an idea you have, it doesn’t have synthetic diamond needles tens of nanometers in di- a chance to come to fruition,” he says. ameter and a few hundred nanometers in length on a Through the I-Corps, researchers could submit a silicon surface (8). Whereas bulk diamond would typ- short proposal to take their existing research beyond ically fracture if pushed beyond a strain of ∼0.15%, the publications. “If your proposal is accepted you’ll re- nanoneedles of diamond could be experimentally ceive a small grant, on the order of $50,000, for a short bent all of the way up to a local maximum strain of period of time—six months to one year—to explore if more than 9% and still return to their original shape. your idea has any chance of going further,” says “ Suresh. After a year of funding, researchers could To our surprise, we could actually bend the needle ” “ evaluate whether their idea had any chance of suc- like you would bend a paperclip, says Suresh. We ceeding, in which case they could found a company or had to videotape the experiment to convince ou- look for outside funding to take the idea further. “NSF rselves and others that you can actually bend dia- ” is just a facilitator, to enable the connections and the mond, he says. Independent validation followed networking,” says Suresh. within a year when a group in China reproduced the Suresh launched I-Corps in 2011 with $6 million of results using natural diamond (9). the NSF’s then $7 billion budget, but the initiative has Bending diamond is not just a matter of intellectual since come a long way. “To my pleasant surprise, it curiosity. Diamond has appealing properties not only has become one of the most successful programs as the hardest material found in nature, but also as a now,” says Suresh. I-Corps now has an annual budget semiconductor. Previous research had shown that of $30 million and has funded more than 1,200 pro- straining silicon could improve its semiconductor jects between 2012 and 2018 across 247 United properties by changing its band gap. “If we can bend States universities, which directly led to 577 compa- a nanoscale diamond by 9%, maybe you can change nies. The program has spawned numerous imitators, the band gap by straining on demand without not just at other United States agencies, such as the changing chemistry,” says Suresh. Modulating the Department of Energy and the National Institutes of band gap of diamond solely through mechanical Health, but across the world, including in Ireland, means could lead to numerous practical applications Australia, and Singapore. “They all have I-Corps–like in solar cells, optoelectronics, and microelectronics. programs now,” says Suresh. “So this is one of the In a 2019 article (10), Suresh and his collaborators most satisfying things I did at the NSF,” he says. showed computationally that straining diamond could After his stint at the NSF, Suresh became president potentially change its band gap from 5.6 eV to ∼2to3 of Carnegie Mellon University in 2013 and launched eV, bringing it within the range of currently used

Ravindran PNAS | October 13, 2020 | vol. 117 | no. 41 | 25193 Downloaded at MIT LIBRARIES on October 30, 2020 semiconductor materials, such as silicon carbide and meets computer science meets mathematics and data gallium nitride. But Suresh was not content to stop there. analytics and artificial intelligence,” he says. “Inter- In his Inaugural Article (1), Suresh explored disciplinary research has come a long way from when I whether straining diamond could reduce its band gap first went to Brown in the 1980s, where even me- down to zero, essentially making it behave like a chanical engineers working with materials scientists metal. He also wondered if he could achieve this feat was a very big deal,” says Suresh. under strains that had already been shown experi- For all his success across varied disciplines, Suresh mentally and without triggering a phase change that cherishes his mechanical engineering roots, and one would convert diamond into graphite. “We showed of his latest honors harkens back to those roots. Suresh using machine learning that the answer to all of those is the recipient of the 2020 American Society of Me- questions is yes,” says Suresh. “Using amounts of chanical Engineers (ASME) medal, the highest honor strain that are already known to be possible experi- given annually to a single individual chosen from the mentally, you can make the band gap of diamond society’s global membership of more than 100,000. vanish,” he says. The same method could be used to He says the award brings back nostalgic memories of improve the properties and performance of most joining ASME as a student member, when he first semiconductor materials with information, communi- came to Iowa State University in the late 1970s at the cation, and energy applications, says Suresh. start of his illustrious career. “It’s very special to re- This work continues Suresh’s long tradition of ceive that from a society that I’ve been part of far more multidisciplinary science. “This is materials science than 40 years,” he says.

1 Z. Shi et al., Metallization of diamond. Proc. Natl. Acad. Sci. U.S.A. 117, 24634–24639 (2020). 2 S. Suresh, Fatigue of Materials, (Cambridge University Press, 2nd Ed., 1998). 3 L. B. Freund, S. Suresh, Thin Film Materials: Stress, Defect Formation and Surface Evolution, (Cambridge University Press, 2004). 4 G. Bao, S. Suresh, Cell and molecular mechanics of biological materials. Nat. Mater. 2, 715–725 (2003). 5 Y. Park et al., Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum. Proc. Natl. Acad. Sci. U.S.A. 105, 13730–13735 (2008). 6 E. Du, M. Diez-Silva, G. J. Kato, M. Dao, S. Suresh, Kinetics of sickle cell biorheology and implications for painful vasoocclusive crisis. Proc. Natl. Acad. Sci. U.S.A. 112, 1422–1427 (2015). 7 I. V. Pivkin et al., Biomechanics of red blood cells in human spleen and consequences for physiology and disease. Proc. Natl. Acad. Sci. U.S.A. 113, 7804–7809 (2016). 8 A. Banerjee et al., Ultralarge elastic deformation of nanoscale diamond. Science 360, 300–302 (2018). 9 A. Nie et al., Approaching diamond’s theoretical elasticity and strength limits. Nat. Commun. 10, 5533 (2019). 10 Z. Shi et al., Deep elastic strain engineering of bandgap through machine learning. Proc. Natl. Acad. Sci. U.S.A. 116, 4117–4122 (2019).

25194 | www.pnas.org/cgi/doi/10.1073/pnas.2018742117 Ravindran Downloaded at MIT LIBRARIES on October 30, 2020 Metallization of diamond

Zhe Shia,b,1, Ming Daoa,1,2, Evgenii Tsymbalovc, Alexander Shapeevc,JuLia,b,2, and Subra Suresha,d,2

aDepartment of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; bDepartment of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; cSkolkovo Institute of Science and Technology, 121205 Moscow, Russia; and dNanyang Technological University, 639798 Singapore, Republic of Singapore

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2012.

Contributed by Subra Suresh, August 7, 2020 (sent for review July 8, 2020; reviewed by Javier Llorca and Nicola Marzari) Experimental discovery of ultralarge elastic deformation in nano- 2) What are the strain states and the lowest strain energy density scale diamond and machine learning of its electronic and phonon required to achieve such “safe” bandgap metallization among structures have created opportunities to address new scientific all possible combinations of straining? questions. Can diamond, with an ultrawide bandgap of 5.6 eV, be 3) How much of such “safe” metallization can be realized within completely metallized, solely under mechanical strain without deformation conditions that have already been shown to be phonon instability, so that its electronic bandgap fully vanishes? achievable experimentally? Through first-principles calculations, finite-element simulations 4) How do crystallographic and geometric variables influence the validated by experiments, and neural network learning, we show metallization of diamond? here that metallization/demetallization as well as indirect-to-direct 5) What are the conditions that trigger indirect-to-direct bandgap bandgap transitions can be achieved reversibly in diamond below electronic transition, or a competing graphitization phase threshold strain levels for phonon instability. We identify the change, in diamond under straining? pathway to metallization within six-dimensional strain space for different sample geometries. We also explore phonon-instability Here we demonstrate that it is possible to achieve 0-eV conditions that promote phase transition to graphite. These findings electronic bandgap in diamond exclusively through the imposi- offer opportunities for tailoring properties of diamond via strain tion of reversible elastic strains, without triggering phonon in- engineering for electronic, photonic, and quantum applications. stability or phase change (4, 5). This discovery implies that reversible metallization/demetallization is feasible through judi- elastic strain engineering | machine learning | multiscale simulations | cious design of mechanical loading conditions and geometry in metallic diamond | materials under extreme conditions nanoscale diamond. We further show that “safe” metallization can be achieved at elastic strain energy density values on the order of 3 he exceptionally high hardness and stiffness of diamond, along 95 to 275 meV/Å , comparable to what has been demonstrated Twith its many extreme physical properties and biocompatibil- in experiments of reversible deformation of diamond nanopillars ity, make it a desirable candidate material for a wide variety of (1, 2). Our results also reveal that even simple bending of low- mechanical, electronic, photonic, biomedical, and energy appli- index <110>-oriented monocrystalline diamond nanoneedles can cations. Recent experimental discovery (1) has established that effectively reduce the bandgap from 5.6 eV down to 0 eV without monocrystalline and polycrystalline diamond nanoneedles (diam- eter ∼300 nm) can be deformed reversibly to local elastic tensile Significance strains higher than 9% and 3.5%, respectively, at room temperature. These findings have been independently corroborated by Identifying the conditions for complete metallization of dia- subsequent deformation experiments (2) on nanoscale pillars mond solely through mechanical strain is an important scientific produced by focused ion beam slicing of natural diamond speci- objective and technological demonstration. Through quantum mens. Here the largest local tensile strains of 13.4% and 9.6%, mechanical calculations, continuum mechanics simulations vali- respectively, are realized in <100>-and<110>-oriented nano- dated by experiments, and machine learning, we show here that needles (2) of single-crystal diamond during bending, whereas the reversible metallization can be achieved in diamond deformed corresponding maximum local compressive strains of −14% and below threshold elastic strain levels for failure or phase trans- −10.1%, respectively, are observed on the compression side. formation. The general method outlined here for deep elastic These advances offer hitherto unexplored possibilities whereby strain engineering is also applicable to map the strain conditions functional properties of diamond can be purposely tailored and for indirect-to-direct bandgap transitions. Our method and significantly altered through strain engineering. One pathway to findings enable extreme alterations of semiconductor properties accomplish this goal is to develop ab initio calculations and ex- via strain engineering for possible applications in power elec- perimentally validated finite element simulations for reversible tronics, optoelectronics, and quantum sensing. straining. Results from these analyses are then used to train Author contributions: Z.S., M.D., A.S., J.L., and S.S. designed research; Z.S., M.D., and E.T. machine-learning algorithms to find optimized material properties performed research; Z.S., M.D., E.T., A.S., J.L., and S.S. analyzed data; and Z.S., M.D., A.S., for diamond for different geometries and loading conditions by J.L., and S.S. wrote the paper. scanning all possible combinations of deformation states within Reviewers: J.L., IMDEA Materials Institute; and N.M., École Polytechnique Fédérale the general six-dimensional (6D) strain space employing reason- de Lausanne. able computing resources (3). Competing interest statement: Z.S., M.D., J.L., and S.S. are coinventors on a patent appli- Motivated by such possibilities, we focus here specifically on cation based on the invention reported in this paper. addressing the following scientific questions: This open access article is distributed under Creative Commons Attribution-NonCommercial- NoDerivatives License 4.0 (CC BY-NC-ND). 1) Is it possible to metallize diamond at room temperature and 1Z.S. and M.D. contributed equally to this work. pressure, from its natural unstrained state with an ultrawide 2To whom correspondence may be addressed. Email: [email protected], [email protected], electronic bandgap of 5.6 eV to full metallization with 0-eV or [email protected]. bandgap, without phonon instability or structural transforma- This article contains supporting information online at https://www.pnas.org/lookup/suppl/ tion such as graphitization, solely through the imposition of doi:10.1073/pnas.2013565117/-/DCSupplemental. strain? First published October 5, 2020.

24634–24639 | PNAS | October 6, 2020 | vol. 117 | no. 40 www.pnas.org/cgi/doi/10.1073/pnas.2013565117 Downloaded at MIT LIBRARIES on October 30, 2020 phonon instability, at about 10.8% local compressive elastic strain. We first present some 6D strain states in Fig. 1 which make Further bending the nanoneedle can, however, induce phonon the bandgap of diamond vanish without phonon instability or instabilities (5) that lead to irreversible sp3 → sp2 (diamond to graphitization. In the crystallographic [100][010][001] coordinate graphite) phase transition or fracture. Indeed, plasticity induced frame, our calculations show that one such complete and “safe” INAUGURAL ARTICLE by such sp3 → sp2 phase transition has recently been observed in metallization occurs when the local 6D strain state is (0.0536, the large bending of a single-crystalline diamond pillar (6), sub- −0.0206, −0.056, 0.0785, 0.0493, 0.0567). Fig. 1A is a k-space plot stantially agreeing with our calculations. Similar graphitization of the GW electronic band structure for diamond deformed to transition is also seen in nanoindentation experiments (7). Navi- this particular 6D strain state, resulting in a direct metal (see SI gating the treacherous elastic strain space above 80 meV/Å3 or Appendix, Fig. S1 for comparison of GW electronic band struc- at >9% local compressive or tensile principal elastic strain to in- ture with that for DFT). Contours of strain energy density are duce complete metallization in diamond without encountering plotted in two-dimensional (2D) strain space in Fig. 1B where phonon instabilities is a “holy grail” demonstration for power the star symbol in black, represents h = 98.7 meV/Å3. Note that electronics, optoelectronics, and quantum sensing systems. the strains and strain energy density values in Fig. 1 are com- Whether mechanically strained or not, the absence of imagi- parable to the values achieved experimentally (1, 2) in reversible nary phonon frequency for the wavevector in the entire Brillouin ultra-large elastic bending of diamond nanoneedles or pillars. zone is the hallmark of a locally stable crystal lattice (5, 8, 9). If a Fig. 2 further illustrates our discovery of the region of “safe” strained perfect crystal lattice has a stable phonon band struc- metallization of diamond without phonon instability and dem- ture, then at T = 0 K and in the absence of defects such as free onstrates reversible indirect-to-direct bandgap transitions under surfaces, interfaces and dislocations, this lattice is guaranteed to large elastic strains. Possible strain states in the three-dimensional avoid spontaneous phase transition or defect nucleation. Con- (3D) space of normal strains «11, «22,and«33, spanning −20% sequently, phonon stability is the minimal requirement for lattice (i.e., compressive strain of 0.2) to +10% (i.e., tensile strain of 0.1) stability and loading reversibility (5). If such a phonon-stable within which “safe” metallization is induced (highlighted in brown diamond can have zero electronic bandgap, Eg = 0 eV (re- color) are shown in Fig. 2A. Regions of metallization are also duced from Eg = 5.6 eV at zero strain), then this extreme elec- plotted in Fig. 2B in the 2D strain space of «11versus «22, with the tronic material (10) is expected to demonstrate unprecedented other four strain components held fixed (i.e., formed as a result of functional flexibility, from ultrawide bandgap semiconductor to 2D projection out of 3D strain region tessellated by cubes on to the far-infrared and even metallic, in one material, without any the plane «33 = −0.056 in Fig. 2A). The triangle data points of change in chemical composition and possibly under dynamic different colors in Fig. 2B represent results of computational loading. The electronic band structures of diamond under ten- simulations of the effect of mechanical strain on bandgap and PHYSICS sorial strain can be predicted with high accuracy based on ab band structure. Two types of “safe” metallization, direct metal and initio density functional theory (DFT) followed by many-body indirect metal (where the band-edge transition is indirect, i.e., GW (G, Green’s function; W, screened Coulomb interaction) from two different k-points), are identified. The 2D region of di- calculations (11). However, because GW calculations are com- rect metal, shaded in brown, encompasses the strain state repre- putationally expensive, it is necessary to invoke a stress–strain sented by the star symbol, which was discussed in Fig. 1. This zone constitutive law for modeling large elastic deformation of dia- is embedded within the strain space of direct bandgap (blue re- mond in any arbitrary sample geometry, along with fast proxy gion, Fig. 2B). The region of indirect metal, also shaded in brown, models for the electronic and phonon band structures. In this is surrounded by the white zone representing the strain space for work, we employ machine-learning algorithms of band structures indirect bandgap (comprising magenta-colored data points from (3) based on an artificial neural network (NN) approach, so as to our simulation). In Fig. 2C, the GW band structure is plotted in perform coupled ab initio and finite element calculations with the k-space to illustrate such indirect-metal state at point c (Fig. constitutive laws based on NNs (see Methods for details). The 2B) inside this zone of “safe” metallization. Examples of nonzero coupling of this simulation to loading and/or device geometry direct and indirect bandgap cases indicated by the band structure optimization (12) and computer-aided design (13) provides a plots are shown in Fig. 2 D and E, respectively. The area shaded in unique and hitherto unknown pathway to engineer “safe” met- gray outside of the dashed lines is the region of large elastic strains allization in diamond. and unstable metallization where phonon instability leading to

Fig. 1. Metallization of diamond. (A) Electronic band structure k-space plot showing complete closure of bandgap leading to metallization of diamond which is subjected to deformation at a 6D strain state of (0.0536, −0.0206, −0.056, 0.0785, 0.0493, 0.0567) in the [100][010][001] coordinate frame. An entire region of strains exists for the metallization of diamond and a 2D cross-section plot of normal strain components «11 and «22 is illustrated in B. The axes in B are absolute strain component values of «11 and «22, with the other four strain components fixed at −0.056, 0.0785, 0.0493, and 0.0567. Color contours indicate regions of constant elastic strain energy density (h) for different deformation states. The black star symbol denotes the strain energy density value, h = 98.7 meV/Å3, which corresponds to the band structure plot shown in A.

Shi et al. PNAS | October 6, 2020 | vol. 117 | no. 40 | 24635 Downloaded at MIT LIBRARIES on October 30, 2020 defect nucleation and/or phase transition occurs (5). Fig. 2F re- in the [100][010][001] coordinate frame. Despite the possibility of veals pronounced reduction in phonon frequency and the occur- extremely large strain in a <100>-oriented nanoneedle, this ori- rence of soft mode associated with strain point f in Fig. 2B where entation primarily facilitates normal strains (with the shear com- phonon instability and associated phase transition from diamond ponents «23, «13,and«12 being relatively much smaller) and the to graphite takes place. The location of the special strain region resultant maximum bandgap reduction is limited before phonon containing metallization is not unique in a general 6D strain hy- instability is reached, causing fracture or phase transformation (5). perspace and such stratified regions may exist in a broad range of For deformation of the <110>-and<111>-oriented needles, on semiconductors. Our findings offer a systematic strategy in the the other hand, it is relatively easier to initiate both normal and search for strain-engineered semiconductor-to-metal transition, shear strain components necessary for band structure engineering indirect-to-direct bandgap transition, as well as phase transition. (3, 23–25) and the resultant bandgap modulation. In the <111>- Experiments show that diamond nanoneedles exhibit ultra- oriented needles, these strain conditions further facilitate indirect- large elastic bending before fracture (1). Such deformation, to-direct bandgap transitions in diamond. The spatial evolution of resulting in local compressive strains larger than −10% and the “safe” direct bandgap regions in our nanoneedles can be found tensile strains in excess of 9%, is reversible upon release of the in SI Appendix,Fig.S5C. Bending direction is another geometrical load. Here we apply simulations to determine bandgap modu- factor, as shown in SI Appendix,Fig.S5D. For a low-index-oriented lation in bent diamond nanoneedles at maximum local strain needle, we find bending direction has little influence on the max- levels that are known to be experimentally feasible (SI Appendix, imum bandgap reduction in the bent needle. Table S1). Fig. 3A schematically illustrates the method whereby a Beyond the configurations considered here, more complex 3D diamond indenter tip pushes on a diamond nanoneedle to induce loading geometries with holes and notches through topology large deformation (1). The finite element method (FEM) is used optimization (26) and micro- and nanomachining of geometric to simulate the sideward bending moment of the diamond needle features (27, 28) can be designed without exposing the metallized upon contact with the indenter tip and account for nonlinear zone to near-surface regions (29), further increasing possibilities elasticity, orientation of the cubic lattice with respect to the for metallizing diamond. These methods for deep elastic strain needle axis, the bending direction, and possible friction between engineering are equally applicable to map the indirect-to-direct the indenter tip and the needle. bandgap transition locations in diamond for the most general 6D Fig. 3B shows FEM results of local compressive and tensile straining case, as indicated in Fig. 2 A, B, and D. When strained strains of the deformed geometry of <110> diamond nanoneedle, diamond is transformed into a direct bandgap semiconductor, with the maximum compressive and tensile strains of −10.8% and even only locally at the site of maximum strain, it would exhibit a 9.6%, respectively. The accuracy of FEM predictions is validated fundamental enhancement in its optical transitions around the by direct comparison with experimentally measured indentation adsorption edge compared to an undeformed diamond in its load plotted against displacement (1). The corresponding predic- natural state. This transition arises from the absence of phonon tions, from our simulations, of the distribution of bandgap are also involvement (momentum change of electron) in the adsorption or plotted in Fig. 3B. The onset of “safe” metallization appears in the emission process. Since absorbance increases exponentially with severely strained compressive side of the nanoneedle at a local thickness in a material, a light energy conversion device based on strain of −10.8%, as shown in Fig. 3C. The propensity toward direct bandgap semiconductor with a high adsorption coefficient increasingly more metal-like behavior with increasing strain is and rationally engineered bandgap value would require much less independent of friction between the indenter and the nanoneedle thickness to absorb the same amount of light with a variety of (see SI Appendix,Fig.S3). The <110> nanoneedle can withstand wavelengths, from the visible to the far-infrared. These consider- up to 12.1% local tensile strain before incurring phonon instability ations could pave the way for designing high-efficiency photo on the tensile side, at a bandgap of 0.62 eV, as shown in Fig. 3D. detectors and emitters from ultraviolet to the far-infrared on a The maximum attainable local tensile strain of 9.6% on the tensile single piece of diamond. As photons and excitons are the primary side of <110> single-crystal natural diamond samples (2), as tools for quantum information processing, this extreme ability to compared to theoretical predictions of higher values (SI Appendix, mold diamond’s band structure will also be highly consequential Fig. S4 and Table S1), could be attributed to the presence of for quantum sensing and quantum computing applications. dislocations and/or other surface-related defects (14–17). The To perform simultaneous mechanical deformation and electronic compressive side is more tolerant to deformation. The maximum properties evaluation, further studies could combine in situ nano- attainable compressive strain could be on the order of −20% along electromechanical loading experiments inside a transmission elec- a low-index orientation (18), suggesting that there is room for ad- tron microscope with built-in electron energy loss spectroscopy ditional elastic deformation after achieving “safe” metallization in (EELS). It is known (30–32) that EELS is reliable for assessing the compression-dominated regions. Note that due to the zero-point bandgap value (including surface plasmon mapping) as well as motion effect (19) and the Varshni effect (20), for physical exper- indirect-to-direct bandgap transition in diamond. Indentation and iments performed at room temperature, the bandgap of diamond is anviling (compression under extreme pressures) coupled with in situ expected to be even smaller than estimated here by 0.4 to 0.6 eV photoluminescence (33–35) or cathodoluminescence (36) spectros- (21, 22). This understanding leads to the inference that safe met- copy as well as electrical resistivity measurement (37) further add to allization in diamond can occur at elastic strain levels somewhat the toolbox for characterization of mechanically induced properties smaller than indicated by our analysis, making it even more easily including superconductivity of diamond (38–40). achievable than appears from the quantitative results plotted here (see Methods for details). Methods Crystallographic orientation of the nanoneedle axis is another First-Principles Calculations. The Vienna Ab initio Simulation Package (VASP) variable determining the extent of large deformation and the (41) was used for DFT calculations to predict the evolution of bandgap and resultant bandgap modulation. This orientation effect is illus- band structure of diamond subjected to mechanical deformation. We in- trated in SI Appendix, Fig. S5 A and B. Among the three types of voked the generalized gradient approximation in the form of Perdew– – ’ nanoneedles studied, the <110>- and <111>-oriented nano- Burke Ernzerhof s (PBE) exchange-correlation (42) functional and the projector augmented wave method (43) in our DFT computation. A plane-wave needles require relatively smaller tensile strains to reduce bandgap < > basis set with an energy cutoff of 600 eV was adopted to expand the elec- through straining, whereas the 100 orientation is the hardest tronic wavefunctions. The Brillouin zone integration was conducted on a orientation to reduce bandgap below 2 eV or approach metalli- 13 × 13 × 13 Monkhorst–Pack (44) k-point mesh. Atomic coordinates in all of zation. This distinction can be attributed to the difference in the structures were relaxed until the maximum residual force was below flexibility to access all six components of the strain tensor expressed 0.0005 meV/Å.

24636 | www.pnas.org/cgi/doi/10.1073/pnas.2013565117 Shi et al. Downloaded at MIT LIBRARIES on October 30, 2020 INAUGURAL ARTICLE PHYSICS

Fig. 2. Stratification of the strain hyperspace into regions of metallization and bandgap transition in diamond. (A) Metallization in elastically strained diamond for different values of normal strain components «11, «22, and «33, with the other three strain components held fixed. The plane with «33 =−0.056 (colored as light green) cuts the 3D volume and results in a projection onto the «11–«22 2D plane. (B) Detailed characterization of the «11–«22 strain space includes a region of direct metal (brown) strains within the region of direct bandgap (blue) strains and a region of indirect metal (brown) strains within the nonzero indirect bandgap strains (white zone with magenta symbols). The black star in indicates the same strain case (0.0536, −0.0206, −0.056, 0.0785, 0.0493, 0.0567) discussed in Fig. 1. An alternative visualization of the metallization strains in A is presented in SI Appendix, Fig. S2.(C) GW band structure of the diamond strained within the “safe” metallization region resulting in an indirect metal. Strained diamond (D) with a direct bandgap (point d in B) and (E) with an indirect bandgap (point e in B). The strain region of phase transformation in diamond (usually associated with phonon instability) is shaded in gray in B.(F) A phonon density of states (DOS) plot corresponding to point f in B illustrates imaginary phonon frequencies (indicated by the magenta arrow) when structural instability occurs. (Inset) A magnified view near zero frequency.

Many-body GW corrections were performed when bandgap evaluations were used for DFT and GW calculations. All band structures were plotted by were needed. It is known that an extremely accurate GW calculation would VASP with a Wannier90 interface (50–52). involve choosing “infinitely” large values for several interdependent pa- We also acknowledge that, even at 0 K, due to the quantum zero-point rameters (45, 46). Given the situation that we need to construct a huge motion, further corrections need to be made to the electronic levels of di- dataset of GW bandgaps for machine-learning purposes and conduct many amond. This renormalization of bandgap could be −0.6 eV to −0.4 eV for calculations for varied 6D strain cases, we hereby struck a balance between undeformed diamond (21, 22). We consider this correction value to be q × × efficiency and effectiveness. Specifically, we chose the -grid to be 6 6 6, negative in other cases of our interest. According to the temperature- the screened cutoff to be 600 eV, and the number of bands for both di- dependent “adiabatic Allen–Heine formula” (19, 53), by setting T = 0to electric matrix calculation and Coulomb hole summation to be 600. In ad- zero-out the Bose–Einstein occupancy factors, the zero-point renormaliza- dition, beyond the single-shot G0W0 method, we allowed two to three tion of the band structure (ΔEZP ) arising from the electron-phonon inter- iterations of the Green’s function in our calculations to obtain accurate nk action could be expressed as quasi-particle shifts. This partially self-consistent GW0 calculation is known to yield results that are in agreement with available experimental measure- ⃒ ⃒ ⃒ ⃒2 ’ (k q) ment for semiconductor materials (47) and better than plain DFT calculations q gnn ν , Δ ZP ≡ Δ ( = ) = ∑∫ d [∑ ] + ΣDW Enk Enk T 0 nk , using hybrid functionals (48). For undeformed diamond, our calculation indi- Ω « k − « ’ k+q ν BZ n’ n n cates a +1.5-eV GW correction to the DFT–PBE bandgap, which matches values

reported in recent literature (49). For general 6D strain cases, this correction where «nk is the single-particle eigenvalue of an electron with crystal mo- may vary (see SI Appendix,Fig.S1for an example). Diamond primitive cells mentum k in the band n, the integral is over the Brillouin zone of volume

Shi et al. PNAS | October 6, 2020 | vol. 117 | no. 40 | 24637 Downloaded at MIT LIBRARIES on October 30, 2020 Fig. 3. Metallization in diamond nanoneedles. (A) Schematic of the bending of single-crystalline diamond nanoneedle by diamond nanoindenter tip inside a scanning electron microscope. (B) FEM predictions of the local compressive and tensile strain distributions (left and middle needle, respectively) and predictions by the machine-learning algorithm of the distribution of bandgap (right needle) for a diamond nanoneedle with its <110> crystallographic direction aligned with the needle axis. (Inset) A scanning electron micrograph of the deformed nanoneedle during the bending experiment, from ref. 1. Reprinted with permission from AAAS. (C) Increasing magnitude of bending in the <110> nanoneedle causes a significant reduction in bandgap of diamond from 5.6 eV (zero strain) down to 0 eV for a maximum local compressive strain of −10.8% (the corresponding maximum local tensile strain on the tension side is 9.6%). (D) Local tensile strain beyond 12.1% results in fracture or graphitization on the tensile side of the nanoneedle according to our ab initio calculations, even when there are no preexisting defects. See also Movie S1 for the evolution of elastic strain energy, bandgap, and the corresponding band structure at the maximum compression site in the nanoneedle, showing the medialization process.

ΩBZ, the outermost summation is over all phonon branches ν, and the first- Machine Learning. The bandgap distribution in diamond nanoneedles de- – (k q) order electron phonon matrix elements gnn’ ν , describe the scattering formed to different strains was computed using machine-learning algo- from an initial state with wave vector k to a final state with wave vector rithms. This is done by representing deformation as a strain tensor and using k + q, with the emission or absorption of a phonon with crystal momentum q an artificial NN to fit the strain states against respective bandgap values belonging to the phonon branch ν. The first term on the right-hand side is obtained accurately by first-principles calculations. The NN fitting is imple- – ΣDW – mented within the TensorFlow framework, an end-to-end open-source the Fan Migdal self-energy term (54) and the nk term is the Debye Waller (DW) self-energy term. Given the DW term are normally much smaller than machine-learning platform released by Google (58). The specific design, the Fan-Migdal term [about 1:5 in diamond (21)], the deciding factors to the similar to our previous work (3), involves a feed-forward architecture with

Δ ZP « − « ’ hidden layers capable of learning the variations of band structure and sign of Enk are the denominators nk n k+q. The change of bandgap can be qualitatively evaluated by considering the relative shift of the valence bandgap with respect to large mechanical deformation. In order to inte- band maximum (VBM) and conduction band minimum (CBM). For VBM, we grate both the PBE and GW datasets we prepared by first-principles calcu- can further assume the coupling primarily comes from scattering within the lations and to produce more consistent and accurate machine learning « outcomes, the same “data fusion” technique as in our work in ref. 3 was valence bands. Since no values of n’ k+q in the valence bands can be larger « « − « used. It took the quantitative advantage of PBE and the qualitative advan- than n k, the denominators n k n’ k+q would always be positive and VBM VBM tage of GW by interpolating between them to achieve decent NN fitting Δ ZP « − « ’ the resultant E k would also be positive. Similarly, n k n k+q at CBM 4 3 nVBM CBM results with only ∼10 PBE and ∼10 GW calculations, successfully alleviat- and the resultant ΔEZP would always be negative. The upward shift of nCBM k ing the need for the otherwise impractical submillion-level amount of VBM and downward shift of CBM would, therefore, result in an overall re- computations. duction in the computed bandgap of diamond. Therefore, from this perspective, we provided a generally conservative estimation of the strain Finite Element Modeling. The ABAQUS (Dassault Systèmes Simulia Corp.) magnitude required for engineering the bandgap. The actual bandgap may software package was employed to conduct FEM analyses on specimen be even smaller than we predicted at particular strain levels as in Fig. 3, models, which replicated the 3D geometry of the diamond nanoneedles. allowing metallization to be safely achieved more easily. Both the cube corner indenter and the nanoneedle were specified as de- To identify the phonon instability boundaries, we performed phonon formable solids using the same elastic properties. A frictional sliding contact stability calculations for densely sampled strain points in 3D or 2D strain was specified between the nanoneedle surface and the indenter surface. space. These calculations were primarily carried out using the VASP-Phonopy Geometric nonlinearity induced by large deformation was accounted for. package (55); 3 × 3 × 3 supercells were created, and phonon calculations Neo-Hookean nonlinear elasticity model was used to simulate large defor- were conducted with a 3 × 3 × 3 k-point mesh. Whenever accurate phonon mation. The equivalent small-strain Young’s modulus was given as 1,100 GPa stability check was needed for diamond primitive cell, density functional and the Poisson’s ratio 0.0725 (1). Since friction makes a negligible change to perturbation theory (56) as implemented in Quantum ESPRESSO (57) was the deformed shape, the friction coefficient between the nanoneedle and adopted, with a dense 11 × 11 × 11 k-grid and 6 × 6 × 6 q-grid. the indenter was taken to be 0.1.

24638 | www.pnas.org/cgi/doi/10.1073/pnas.2013565117 Shi et al. Downloaded at MIT LIBRARIES on October 30, 2020 Data Availability. Data supporting the findings of this study are available in an Office of Science User Facility operated for the US Department of the paper and SI Appendix. Energy Office of Science by Los Alamos National Laboratory (Contract 89233218CNA000001) and Sandia National Laboratories (Contract DE-NA-

ACKNOWLEDGMENTS. We acknowledge support from the Office of Naval 0003525). M.D. acknowledges support from MIT J-Clinic for Machine Learn- INAUGURAL ARTICLE Research Multidisciplinary University Research Initiative grant N00014-18-1- ing and Health. S.S. acknowledges support from Nanyang Technological 2497. Z.S. and E.T. acknowledge support by the Massachusetts Institute of University through the Distinguished University Professorship. We thank Technology (MIT) Skoltech Next Generation Program 2016-7/NGP. E.T. and Dr. Hua Wang from MIT for conducting independent computational checks A.S. acknowledge support by the Center for Integrated Nanotechnologies, and verifications.

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Shi et al. PNAS | October 6, 2020 | vol. 117 | no. 40 | 24639 Downloaded at MIT LIBRARIES on October 30, 2020 Metallization of diamond

Zhe Shi,1,2* Ming Dao,1*† Evgenii Tsymbalov,3 Alexander Shapeev,3 Ju Li,1,2† Subra Suresh1,4† 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; 2Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; 3Skolkovo Institute of Science and Technology, 121205 Moscow, Russia; and 4Nanyang Technological University, 639798 Singapore, Republic of Singapore *These authors contributed equally. †Corresponding author. Email: [email protected] (S.S.); [email protected] (J.L.); [email protected] (M.D.)

Supplementary Materials

This PDF file includes: Figs. S1 to S5 Table S1 Caption for Movie S1 References for SI reference citations

Other supplementary materials for this manuscript include the following: Movie S1

Supplementary Figures and Tables

PBE GW

0 Energy (eV) Energy

-10 0.5 = 0 0.5    Fig. S1. Deformed diamond band structures plotted in the scheme of DFT-PBE and GW. The 6D strain case is the same as in Fig. 1A. There is about +0.68 eV GW correction in the DFT-PBE bandgap at this particular case.

www.pnas.org/cgi/doi/10.1073/pnas.2013565117 Fig. S2. Spiderweb-plot illustrating the metallization strain cases (colored as cyan webs) in the 3D space of normal strains 𝜀, 𝜀 and 𝜀 spanning −20% (i.e. compressive strain of 0.2) to +10% (i.e. tensile strain of 0.1), with shear components 𝜀, 𝜀, 𝜀 all fixed to be constants as in Fig. 2A. Strain components of the same magnitude belong to the same concentric circle in the plot.

Fig. S3. Machine learning prediction of the bandgap distribution for the same <111> nanoneedle bent by the same amount and friction coefficient μ from 0 (perfectly smooth contact) to 1. The propensity of bandgap reduction during deformation is seen from our simulations to be independent of the level of friction between the indenter and the nanoneedle. Fig. S4. FEM predictions of the local maximum principal (compressive/tensile) strain distributions and machine learning predictions of the bandgap distribution for the <110> oriented diamond nanoneedle deformed at the theoretically approachable maximum tensile strain of 12.1%.

Fig. S5. Orientation dependent bandgap changes and indirect-to-direct bandgap transitions. (A) Reduction of the lowest bandgap as a function of strain in nanoneedles of <100> and <110> orientations, respectively. (B) The definition of the reference crystal orientation for the three diamond nanoneedle families: [010]/[001] for a [100] needle, [110]/[001] for a [110] needle, and [121]/[101] for a [111] needle. The green triangle indicates the (111) plane for the <111> nanoneedle. (C) Reduction of the lowest bandgap (left axis) and development of direct bandgap region volume (right axis) in nanoneedles of <111> orientation. These volumes are colored in red on the tensile side of the bent needles plotted next to the data points. Graphitization occurs in the nanoneedle right after 8.8% local tensile strain, as indicated by the grey region. The direct bandgap region volume is expressed in terms of the number of FEM nodes that correspond to a direct bandgap. (D) Schematic showing an as-grown, aligned, and bent nanoneedle. With the crystal orientation along the needle longitudinal direction known (blue arrows), the positioning angle 𝜑 defines the pre-selected crystal coordinates (black dotted arrows) versus the selected reference crystal coordinates (red arrows). 𝜑 is modulated by rotating the substrate in the alignment stage, introducing an additional degree of freedom and many more combinations of strain states in the bent needle. The needle is then bent when pushed by the side surface of a cube corner indenter tip, as described in Ref. (1). Small blue arrows along the needle in the deformed configuration indicate the local crystallographic needle axis.

Table S1: Limits for elastic strains and strain energy density from experiments (1–3) and calculations. The deformation of nanoneedle is limited by tension, i.e., failure first takes place on the tensile side of the nanoneedle. The strains listed below for the compressive strains in the nanoneedle correspond to the point at which failure first occurs on the tensile side of the nanoneedle. Since higher compressive strains can be achieved without failure in pure compression of diamond, the compressive strains listed below are lower bound estimates.

Crystallographic Theoretical limit for bending diamond Theoretical limit for Experimental results orientation of nanoneedle (for experimental configuration) “safe” metallization diamond in general 6D strain Tensile side Compressive side Tensile side Compressive side nanoneedle space (this study) <100> 13.4% -14.0% - - <110> 9.6% -10.1% 12.1% -14.5% ≤ 98.7 meV/Å3 <111> 8.8% -9.9% 8.8% -27.0%

Supplementary Movie

Movie S1: The evolution of elastic strain energy density, bandgap and the corresponding band structure at the maximum compression site in the nanoneedle, showing the metallization process of the diamond nanoneedle shown in Fig. 3 under bending.

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